emendes

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7 years, 277 days

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These are questions asked by emendes

Hello

After getting help from users on this list, I wrote an example on how to iterate a discrete map using a given initial condition as follows:

restart:with(ListTools):
NestList := proc (f, x, n::nonnegint, nprec::posint := 10) local R, k; R := rtable(0 .. n, [x]); Digits := nprec; for k to n do R[k] := expand(f(R[k-1])) end do; [seq(R)] end proc:
logistic := proc (x) options operator, arrow; 4*x*(1-x) end proc:
fp := [solve((logistic@@5)(x) = x, x)]:
cfp := allvalues(fp[5]);
nstep:=12:
p := nstep+50; 
aaa := Flatten(map(`~`[Re], evalf(NestList(logistic, evalf(cfp), p)))); 
dat := [seq([i-nstep-1, aaa[i]], i = 1 .. p)]; 
plot(dat, style = pointline, symbol = solidcircle, symbolsize = 4, thickness = 0, view = [default, 0 .. 1]);

The result should be a period 5 and some chaotic data due to machine precision. However the trajectory ejected to infinity. I have tried with a different initial condition, say 0.1, and it worked just fine. Even if the precision is increased, the trajectory (orbit) will eventually eject to infinity.  I couldn't spot what is wrong.

I am running Maple 2017 on linux and on a mac. 

Many thanks

Ed

 

Hello

I am definitely missing something on how Maple deals with functions and outputs.  I need to define a new function using an output of a previous calculation but I didn't figure out how to do it. 

 

aux := rsolve({y(0) = y0, y(n) = 4*y(n-1)*(1-y(n-1))}, y(n));
solucao := (n,y0)-> aux;
solucao(3,1/2);

Neither n nor y0 are replaced for the given values.  What am I missing?

 

Many thanks

 

Ed

 

Hello

I am revising the unstable period orbits of the Logistic map, y[n]=4*y[n-1]*(1-y[n]), in Maple.  Although I have implemented the equation and use a loop for the iterations, I wonder whether there is a faster and concise way to code the equation in Maple. 

Here it is what I did:

y[0] := (-sqrt(5)+5)*(1/8);

for n to 10 do y[n] := 4*y[n-1]*(1-y[n-1]) end do;
soly := [seq(simplify(expand(y[n]), radical), n = 0 .. 10)];
dat := [seq([n, Re(evalf(soly[n]))], n = 1 .. 10)]; plot(dat, labels = ["k", "x(k)"], style = pointline,title="Period 2");

Since only few iterations are needed, the solution is symbolic (and then convert to float).  

Many thanks.

Ed

 

 

Hello

I wonder how I could use Maple commands to do the following:

An irrational number, ir, (a huge symbolic expression as a result of iterating a discrete map) is converted to single precision (Real16) and then to hexadecimal as a string. Example: using matlab it will be something like single(ir)=0.25(float representation) =3e800000 (hexadecimal representation).

I am not sure if single precision is available in Maple 2017 but I guess Real32, Real64 and Real128 are.

Once the hexadecimal representation is acquired I need to convert it back to Real16, Real 32 and etc.

Your help is much appreciated.

Many thanks

Ed

Hello

I wonder how I could use maple to manipulate a symbolic matrix.  For instance, I need to calculate the transpose of the following matrix:

 

Matrix(2, 2, [[Transpose(X)+X-Q, A . X], [Transpose(X) . Transpose(A), Q]])

 

where X, Q and A are matrices of unknown (but compatible) size.  Of course, the main problem is how  X, Q and A should be defined to allow maple to calculate the transpose. 

Many thanks.

 

Ed

 

 

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